32.4.25 problem Recognizable Exact Differential equations. Integrating factors. Exercise 10.17, page 90

Internal problem ID [5836]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Exercise 10.17, page 90
Date solved : Sunday, March 30, 2025 at 10:19:08 AM
CAS classification : [_rational]

\begin{align*} y-\left (y^{2}+x^{2}+x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 36

ode:=y(x)-(y(x)^2+x^2+x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {{\mathrm e}^{-2 i y} \left (i x +y\right )+2 c_1 \left (i y+x \right )}{2 i y+2 x} = 0 \]

✓ Mathematica. Time used: 0.117 (sec). Leaf size: 18

ode=(y[x])-(y[x]^2+x^2+x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [y(x)-\arctan \left (\frac {x}{y(x)}\right )=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x**2 - x - y(x)**2)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - y(x)/(x**2 + x + y(x)**2) cannot be solved by the factorable group method